How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?
Solution and Explanation
For x number of resistors of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is given by Ohm's law as \(V= IR\)
\(R= \frac VI\)
Where,
Supply voltage, \(V= 220 \ V\)
Current, \(I = 5\ A\)
Equivalent resistance of the combination = \(R\), given as
\(\frac 1R = x \times (\frac {1}{176})\)
\(R = \frac {176}{x}\)
From Ohm's law,
\(\frac VI = \frac {176}{x}\)
\(x = 176 \times \frac IV \)
\(x= 176 \times \frac {5}{220}\)
\(x= 4\)
Therefore, four resistors of 176 Ω are required to draw the given amount of current.
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Concepts Used:
Resistance
Resistance is the measure of opposition applied by any object to the flow of electric current. A resistor is an electronic constituent that is used in the circuit with the purpose of offering that specific amount of resistance.
R=V/I
In this case,
v = Voltage across its ends
I = Current flowing through it
All materials resist current flow to some degree. They fall into one of two broad categories:
- Conductors: Materials that offer very little resistance where electrons can move easily. Examples: silver, copper, gold and aluminum.
- Insulators: Materials that present high resistance and restrict the flow of electrons. Examples: Rubber, paper, glass, wood and plastic.
Resistance measurements are normally taken to indicate the condition of a component or a circuit.
- The higher the resistance, the lower the current flow. If abnormally high, one possible cause (among many) could be damaged conductors due to burning or corrosion. All conductors give off some degree of heat, so overheating is an issue often associated with resistance.
- The lower the resistance, the higher the current flow. Possible causes: insulators damaged by moisture or overheating.